A gathering of 12 people break into 3 groups of 4 to play 3 different games : carrom, UNO and bridge

Question

A gathering of 12 people break into 3 groups of 4 to play 3 different games : carrom, UNO and bridge. Find the number of ways these $12$ people can be grouped.[1] Aaron and Sandy do not get along with each other and do not want to be in the same group. Find the number of ways these $12$ people can be grouped with this restriction.[3] Given that Aaron and Sandy are not in the same group, find the probability that a third person Billy is in the same group as Aaron.[3]

Accepted Answer

(a)34650 (b)25200 (c) $P(A|B)=\frac{3}{10}$/0.3

2025 ACJC P2 Q7

2025 ACJC P2 Q7